Lecture 27 typed - Lecture 27 Deeper Still: The Hydrogen...

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Lecture 27 Deeper Still: The Hydrogen Connection Review the internal Hamiltonian. 2 2 2 0 2 4 2 2 2 2 2 0 ( , , ) ( , , ) where ( , , ) ( ) ( , ) 2 4 and E a.u. 8 2 We should be familiar with all our quantum numbers from freshman chemistry (1s, 2p, 3d, etc.) Th r nl lm n Ze r E r r R r Y r Z e Z h n n ψ θ ϕ θ φ μ πε ε ∇ − = = = = a is is where they come from! is the principal quantum number governs the letter of the atomic orbital and determines the orbital magnetic direction ( i.e. vs. ) x y n l m p p An important observation is that in this one-electron atom all orbitals in a given energy level are degenerate as shown at left. The number of degenerate states given by 1 2 0 (2 1) n l l n = + = . Also it is important to note that in multi- electronic atoms the degeneracy amongst the orbitals breaks.
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Now we will discuss the Bohr model with respect to the true quantum mechanical model. The first interesting observation about the Bohr model is that it predicts the correct
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Lecture 27 typed - Lecture 27 Deeper Still: The Hydrogen...

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